Ultimately, if you want to know whether a particular photographer's work is genuinely from the wild, you need to check into their body of work. Ideally, they'll be honest about the use of such animal parks - for the overwhelming majority of cases, though, if they claim the subjects to be wild, they will be.

That's not to say the photos won't have been processed, of course - that's entirely up to individual taste, whether that's casting it to monochrome, or boosting the contrast to bring out the skin texture of an elephant.

In photography circles, parks like those are promoted as a means for enthusiasts to see species they'd otherwise have to travel great distances for - rather like a cageless zoo. It's not something I've engaged in[1], but I can understand the appeal from a hobbyist perspective; and understandably, if you're looking for "wildlife" photography on demand, perhaps for an advertising campaign, you're unlikely to commission someone to attempt to obtain just the right photo out in the wild.

[1] My wildlife focus is primarily rabbits, eg "Momentary":

https://www.flickr.com/photos/porsupah/9495186995/